Electromagnetic knot applications in radio waves for wireless and photonics for quantum computing

ABSTRACT

A system for transmitting signals includes processing circuitry for receiving at least one input signal for transmission from the processing circuitry to a second location. Electromagnetic knot processing circuitry receives processed signals from the first processing circuitry and applies an electromagnetic knot to the received processed signal before transmission to the second location. A first signal degradation caused by environmental factors of the electromagnetic knot processed signal is improved over a second signal degradation caused by the environmental factors of a non-electromagnetic knot processed signal.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Patent Application Ser. No.62/744,516, filed Oct. 11, 2018, entitled ELECTROMAGNETIC KNOTS AND ITSAPPLICATIONS IN RADIO WAVES FOR WIRELESS AND PHOTONICS FOR QUANTUMCOMPUTING, which is incorporated by reference herein in its entirety.

TECHNICAL FIELD

The present invention relates to the transmission signals in wirelesscommunication systems and quantum computers, and more particularly to amanner for improving signal degradation in wireless communicationssystems and quantum computers using electromagnetic knots.

BACKGROUND

The transmission of wireless signals in the optical and RF environmentand the transmission of quantum signals within a quantum computingenvironment is susceptible to various environmental interferences anddegradations. These environmental interferences and degradations canharm signal quality and cause problems with signal interpretation anddiscernment. Some manner for limiting signal degradations in theseoperating environments would provide a great deal of improvement in thesignal transmissions and quantum computing environments.

SUMMARY

The present invention, as disclosed and described herein, in one aspectthereof comprises a system for transmitting signals includes processingcircuitry for receiving at least one input signal for transmission fromthe processing circuitry to a second location. Electromagnetic knotprocessing circuitry receives processed signals from the processingcircuitry and applies an electromagnetic knot to the received processedsignal before transmission to the second location. A first signaldegradation caused by environmental factors of the electromagnetic knotprocessed signal is improved over a second signal degradation caused bythe environmental factors of a non-electromagnetic knot processedsignal.

BRIEF DESCRIPTION OF THE DRAWINGS

For a more complete understanding, reference is now made to thefollowing description taken in conjunction with the accompanyingDrawings in which:

FIG. 1 illustrates various problems associated with wirelesscommunications that may be address by electromagnetic knots;

FIG. 2 illustrates problems associated with quantum computing that maybe addressed by electromagnetic knots;

FIG. 3 illustrates the combination of generated signals withelectromagnetic knot processing for generating more resilient signals;

FIG. 4 illustrates a wireless signal transmission system havingelectromagnetic knot processing applied thereto;

FIG. 5 illustrates an optical signal transmission system havingelectromagnetic knot processing applied thereto;

FIG. 6 illustrates a quantum computing system having electromagneticprocessing applied thereto;

FIG. 7 illustrates various methods for electromagnetic knot generation;

FIG. 8 illustrates a general block diagram of the manner for generatingelectromagnetic radio wave knots;

FIG. 9 illustrates electrically conducting rings for generation ofelectromagnetic radio wave knots;

FIG. 10 illustrates a functional block diagram of a of a structure forgenerating wireless knots using a toroidal antenna;

FIG. 11 illustrates a solenoid wrapped toroidal ring;

FIG. 12 illustrates a group of solenoid wrapped toroidal rings;

FIG. 13 illustrates a first sophisticated solenoid wrapped toroidal ringstructure;

FIG. 14 illustrates a second sophisticated solenoid wrapped toroidalring structure;

FIG. 15 illustrates the use of three-dimensional patch antennas forapplying electromagnetic knots;

FIG. 16 illustrates a top view of a multilayer patch antenna array;

FIG. 17 illustrates a side view of a multilayer patch antenna array;

FIG. 18 illustrates a first layer of a multilayer patch antenna array;

FIG. 19 illustrates a second layer of a multilayer patch antenna array;

FIG. 20 illustrates a transmitter for use with a multilayer patchantenna array;

FIG. 21 illustrates a multiplexed OAM signal transmitted from amultilayer patch antenna array;

FIG. 22 illustrates a receiver for use with a multilayer patch antennaarray;

FIG. 23 illustrates a system for multiplexing and demultiplexing OAMknotted signals;

FIG. 24 illustrates a circuit for multiplexing OAM knotted beams withother radio channels; and

FIG. 25 illustrates knot division multiplexing circuitry.

DETAILED DESCRIPTION

Referring now to the drawings, wherein like reference numbers are usedherein to designate like elements throughout, the various views andembodiments of electromagnetic knot applications in radio waves forwireless transmissions and photonics for quantum computing areillustrated and described, and other possible embodiments are described.The figures are not necessarily drawn to scale, and in some instancesthe drawings have been exaggerated and/or simplified in places forillustrative purposes only. One of ordinary skill in the art willappreciate the many possible applications and variations based on thefollowing examples of possible embodiments.

An exact solution of Maxwell's equations in empty space with non-trivialtopology of the force lines has been obtained by Arrayas and Trueba asdescribed in M. Arrayas and J. L. Trueba, Ann. Phys. (Berlin) 524, 71-75(2012), which is incorporated herein by reference in its entirety, inwhich there is an exchange of helicity between the electric and magneticfields. The two helicities are different at time zero, but in the limitof infinite time they are equal, their sum being conserved. Although notwidely known, there are topological solutions of Maxwell equations withthe surprising property that any pair of electric lines and any pair ofmagnetic lines are linked except for a zero measure set. These solutionscalled “electromagnetic knots”, discovered and described in A. F.Rañada, Lett. Math. Phys. 18, 97 (1989); A. F. Rañada, J. Phys. A: Math.Gen. 23, L815 (1990); A. F. Rañada, J. Phys. A: Math. Gen. 25, 1621(1992), which are each incorporated herein by reference in theirentirety and building on the Hopf fibration as describe in H. Hopf,Math. Ann. 104, 637 (1931), which is incorporated herein by reference inits entirety allows for the basis for a topological model ofelectro-magnetism (TME) to be proposed, in which the force lines play aprominent role. In A. F. Rañada and J. L. Trueba, Modern NonlinearOptics, Part III. Electromagnetism, Vol. 119, edited by I. Prigogine andS. A. Rice (John Wiley and Sons, New York, 2001) pp. 197-253 and A. F.Rañada, Phys. Lett. A 310, 134 (2003), each of which are incorporatedherein by reference in their entirety, a review is presented of the workdone on the topological model of electro-magnetism. The paper by Arrayasand Trueba is an important step in its development.

The principal aim of this line of research is to complete thetopological model of electro-magnetism that, in its present form, islocally equivalent to Maxwell's theory, is based on the topology of theelectric and magnetic lines and has topological constants of motion asthe electric charge or the total helicity. The force lines are the levelcurves of two complex scalar fields ϕ(r, t), θ(r, t) with only one valueat infinity, that can be interpreted as maps between two spheres S³⋅→S²,the compactification of the physical 3-space and the complete complexplane. As shown by Hopf, such maps can be classified in homotopyclasses. W. T. M. Irvine and D. Bouwmeester, Nature Phys. 4, 716 (2008),which is incorporated herein by reference, describes some excitingmathematical representations of these knots, analyzes their physicalproperties and considers how they can be experimentally constructed.

Faraday dedicated many hours to thinking about the idea of force lines.In his view they had to be important since the experiments showed that asort of unknown perturbations of space occurred along them. In fact,during the 19th century many physicists tried to understand theelectromagnetic phenomena in terms of the vorticity and the streamlinesof the ether. Then in 1869, Kelvin wrote a paper entitled “On vortexatoms” (Lord Kelvin, Trans. R. Soc. Edin-burgh 25, 217 (1869), which isincorporated herein by reference) suggesting that the atoms could belinks or knots of the vacuum vorticity lines, an idea praised by Maxwellin his explanation of the term “atomism” in the Encyclopaedia Britannicain 1875. Kelvin disliked the extended idea that the atoms are infinitelyhard and rigid objects, which he qualified as “the monstrousassumption.” He was much impressed by the constancy of the strength ofthe vorticity tubes in a non-viscous fluid that Helmholtz hadinvestigated. For him, this was an unalterable quality on which theatomic theory could be based without the need for infinitely rigidobjects. We know today that this is also a property of topologicalmodels in which invariant numbers characterize configurations that candeform, warp or distort. About sixty years later, topology appeared inDirac's significant proposal of the monopole (P. A. M. Dirac, Proc. R.Soc. Lond. A 133, 60 (1931), which is incorporated herein by reference)and later in the Aharonov-Bohm effect (Y. Aharonov and D. Bohm, Phys.,Rev. 115, 485 (1959), which is incorporated herein by reference) whichshow that, in order to describe electromagnetic phenomena, topology isneeded. The same idea motivated the insightful statement attributed toAtiyah “Both topology and quantum physics go from the continuous to thediscrete” as described in M. Atiyah, The Geometry and Physics of Knots(Cambridge University Press, Cambridge, 1990), which is incorporatedherein by reference.

In the topological model of electro-magnetism, the Faraday 2-form andits dual are equal to the pull-backs of the area 2-form in S², say σ, bythe two maps, i.e.

=½F _(uv) dx ^(μ) dx ^(v)=−ϕ*σ,*

=½*F _(uv) dx ^(μ) dx ^(v)=θ*σWhere * is the Hodge or duality operator, the two scalars verifying thecondition *φ*σ=−θ*σ. It is curious that if this condition is fulfilled,then the forms

and

verify automatically Maxwell's equations. In that case, each solution ischaracterized by the corresponding Hopf index n. The previous relationsallow the expressions of the magnetic field B(r, t) and electric field E(r, t) to be written in terms of the scalars as:

${B( {r,t} )} = {\frac{\sqrt{a}}{2\;\pi\; i}\frac{{\nabla\;\phi} \times {\nabla\;\overset{\_}{\phi}}}{( {1 + {\overset{\_}{\phi}\phi}} )^{2}}}$${E( {r,t} )} = {\frac{\sqrt{a\; c}}{2\;\pi\; i}\frac{{\nabla\;\overset{\_}{\theta}} \times {\nabla\;\theta}}{( {1 + {\overset{\_}{\theta}\theta}} )^{2}}}$where a bar over a variable means a complex conjugate, i is theimaginary unit, c is the speed of light and a is a constant introducedso that the magnetic and electric fields have the correct dimensions. InSI units a is a pure number times

μ₀, where

is the Planck constant, c the light speed and μ₀ the vacuumpermeability. The pure number is taken here to be 1, the simplestchoice.

Some thought-provoking properties of the topological model ofelectro-magnetism are the following. It is locally equivalent to thestandard Maxwell's theory in the sense that any electromagnetic knotcoincides locally with a radiation field, i.e. satisfying E·B=0. Howeverthe two models are not globally equivalent because of the way in whichthe knots behave around the point at infinity. As a consequence of theDarboux theorem as described in C. Godbillon, Géometrie différentielleet mécanique analytique (Hermann, Paris, 1969), which is incorporatedherein by reference, any electromagnetic field is locally equal to thesum of two radiation fields.

Maxwell's equations are equal to the exact linearization by change ofvariables (not by truncation) ϕ, θ→E, B of the set of nonlinearequations of motion of the scalars φ, θ. These equations can be easilyfound, using the standard Lagrangian density of the electromagneticfield expressed in terms of the pair φ, θ. It happens, however, thatthis change of variables is not completely invertible, which introducesa “hidden nonlinearity” that explains why the linearity of the standardMaxwell equations is compatible with the existence of topologicalconstants in the topological model of electro-magnetism.

The electromagnetic helicity

is defined as:

=½∫R ₃(A·B+C·E/c ²)d ³ r,where A and C are vector potentials for B and E, respectively asdescribed in F. W. Hehl and Y. N. Obukhov, Foundations of ClassicalElectrodynamics: Charge, Flux and Metric (Birkhäuser, Boston, 2003),which is incorporated herein by reference. This quantity is conservedand topologically quantized. Solving the integral, it is found that

=na, where n is the common value of the Hopf indices of ϕ and θ. Itturns out, moreover, that

=(N_(R)−N_(L)) where N_(R), N_(L) are the classical expressions of thenumber of right- and left-handed photons contained in the field (i.e.

=∫d³k[ā_(R)(K)a_((k))(k)−ā_(L)(k)a_(L)(k)], a_(R)(k)a_(L)(k), beingFourier transforms of A_(μ) in classical theory but creation andannihilation operators in the quantum version). This establishes thecurious relation n=NR−NL between two concepts of helicity, i.e. therotation of pairs of lines around one another (n, classical) and thedifference between the number of right- and left-handed photons (NR−NL,quantum), respectively. In the standard knots of the topological modelof electro-magnetism, the two terms of the helicity integral are equal.What Arrayás and Trueba have done suggests that these standard knots areattractors of other knots that have unequal electric and magnetichelicities, which is a curious and interesting result as illustrated inM. Arrayás and J. L. Trueba, arXiv:1106.1122v1 [hep-th] (2011), which isincorporated herein by reference.

Another intriguing property of the topological model ofelectro-magnetism is that the electric charge is also topologicallyquantized (as well as the hypothetical magnetic charge), the fundamentalcharge that it predicts being q₀=

cc₀=5.29×10⁻¹⁹ C≈3.3 e, while its fundamental monopole would beg₀=q₀/c=g_(D)/20.75, g_(D) being the value of the Dirac monopole asdescribed in A. F. Rañada and J. L. Trueba, Phys. Lett. B 422, 196(1998), which is incorporated herein by reference. This means that thetopological model of electro-magnetism is symmetric under theinterchange of electricity and magnetism. Note, however, thate<q₀<g_(D)c, which raises an exciting, if perhaps speculative,eventuality. Because the vacuum is dielectric but also paramagnetic, itseffect must be to decrease the value of the charge and to increase thatof the monopole. This suggests the possibility that the topologicalmodel of electro-magnetism could describe what happens at high energies,at the unification scale, where the particles interact directly throughtheir fundamental bare charge q₀ without renormalization. Thissuggestion is reinforced by the fact that the fine structure constant ofthe model is:a0=q ₀ ²/4π

cε ₀=¼π≈0.8, a value 0 close to a strongApplication to Wireless Communications and Quantum Computing

Referring now to FIGS. 1 and 2, there are illustrated the variousproblems associated with wireless communications and quantum computingthat may be address by electromagnetic knots. In wireless communications102 and quantum computing 202, there are natural processes that degradethe signal. In the case of wireless communications 102 this degradationis introduced by fading 104, reflection 106, diffraction 108, scattering110 as well as geometrical dispersion 112. The fading 104 is mostly dueto reflections, refractions and scattering environment which could takethe form of slow fading or fast fading. The geometrical dispersion 112is a function of distance and as the electromagnetic wave propagateslonger distances, the energy and power are reduced. In case of quantumcomputing 202, superposition of states to produce qubits can bedestroyed due to de-coherence 204. Natural processes destroy coherencein quantum computing superposition of states for qubits.

This system and method introduces a new way of combating thedegradations due to fading and geometrical dispersion in wirelesscommunications as well as quantum de-coherence in quantum computingusing electromagnetic knots. As illustrated in FIG. 3 by combiningexisting signals 302 with some type of electromagnetic knot processing304, a more resilient signal 306 is provided that is not as susceptibleto the issues described above is provided. Wireless signal degradationscannot easily open an electromagnetic knot and such electromagneticknots are resistant to channel impairments. Quantum signals having anelectromagnetic knot applied thereto cannot easily be opened and areresistant to de-coherence. The generation of electromagnetic knots 304is more fully described herein below.

In general, natural processes can degrade fabrics and signals, butgenerally they are not able to undue a knotted fabric or a knottedelectromagnetic wave. Today, we know that Maxwell equations have anunderlying topological structure given by a scalar field whichrepresents a map S3×R→S2 that determines the electromagnetic fieldthrough a certain transformation from 3-sphere to 2-sphere. Therefore,Maxwell equations in vacuum have topological solutions, characterized bya Hopf index equal to the linking number of any pair of magnetic lines.This allows the classification of the electromagnetic fields intohomotopy classes, labeled by the value of the helicity. This helicityverifies ∫A·B dr=na where “n” is an integer and an action constant. Thishelicity is proportional to the integer action constant.

Topology will plays a very important role in field theory. Since 1931,when Dirac proposed his idea of the monopole, topological models have agrowing place in physics. There have been many applications such as thesine-Gordon equation, the Hooft-Polyakov monopole, the Skyrme andFaddeev models, the Aharonov-Bohm effect, Berry's phase, or Chern-Simonsterms.

As more fully described hereinbelow, a model is introduced of anelectromagnetic field in which the magnetic helicity ∫A·B dr is atopological constant of the motion, which allows the classification ofthe possible fields into homotopy classes, as it is equal to the linkingnumber of any pair of magnetic lines.

Electromagnetic Field Model with Hopf Index

Let ϕ(r,t) and θ(r,t) be two complex scalar fields representing mapsR³×R→C. By identifying R³∩{∞} with S³ and C∩{∞} with S², viastereographic projection, ϕ and 0 can be understood as maps S³×R→S². Wethen define the antisymmetric tensors F_(uv), G_(uv) to be equal to:

$F_{uv} = {{\int_{uv}(\phi)} = \ {\frac{\sqrt{a}}{2\;\pi\; i}\frac{{{\partial_{u}\phi^{*}}{\partial_{u}\phi}} - {{\partial_{u}\phi^{*}}{\partial_{u}\phi}}}{( {1 + {\phi^{*}\phi}} )^{2}}}}$$G_{uv} = {{f_{uv}(\theta)} = {\frac{\sqrt{a}}{2\;\pi\; i}\frac{{{\partial_{u}\theta^{*}}{\partial_{u}\theta}} - {{\partial_{u}\theta^{*}}{\partial_{u}\theta}}}{( {1 + {\theta^{*}\theta}} )^{2}}}}$where a is an action constant, introduced so that F_(uv), and G_(uv),will have proper dimensions for electromagnetic fields, and prescribethat G be the dual of F or, equivalently,G _(uv)=½ϵ_(uvxβ) F ^(xβ) F _(uv)=−½ϵ_(uvxβ) G ^(xβ)where ϵ⁰¹²³=+1. To fulfill this requirement, ϕ is a scalar and θ apseudo scalar. This allows defining of the magnetic and electric fieldsB and E as:F _(Ot=) =E ₁ , F _(y)=−ϵ_(yk) B _(k) ; G _(oi) =B ₁ , G _(y)=−ϵ_(ijk) E_(k);

After that, the Lagrangian density is determined:L=−⅛(F _(uv) F ^(uv) +G _(uv) G ^(uv)),The duality condition or constraint is then imposed:M _(σβ) =G _(xβ)−½ϵ_(xβuv) F ^(uv)=0

Following the method of Lagrange multipliers, the modified Lagrangiandensity are determined according to:L′=L+μ ^(αβ) M _(αβ),where the multipliers are the component of the constant tensor μ^(xβ). Asimple calculation shows that the constraint above does not contributeto the Euler-Lagrange equations, which happen to be:∂_(α) F ^(αβ)∂_(β)ϕ=0 ∂_(α) F ^(αβ∂) _(β)ϕ*=0∂_(α) G ^(αβ)∂_(β)θ=0 ∂_(α) G ^(αβ)∂_(β)θ*=0

This means that, if the Cauchy data (ϕ, ∂₀ϕ, θ, ∂₀θ) at t=0 verify theconstraint, it will be maintained for all t>0. Surprisingly, it followsthat both F_(αβ) and ∂_(αβ) verify Maxwell equations in vacuum. In fact,definitions above imply that:ϵ^(αβy5)∂_(β) F _(yδϵ) ^(αβy5)∂_(β) G _(yδ)=0, β=0,1,2,3which is the second Maxwell pair for the two tensors. In other words, ϕand θ obey the Euler-Lagrange equations), then F_(αβ) and G_(αβ) definedby verify the Maxwell ones and are, therefore, electromagnetic fields ofthe standard theory. The reason is that Maxwell equations in vacuum havethe property that, if two dual tensors verify the first pair, they alsoverify the second one (i.e. the two pairs are dual to each other).

A standard electromagnetic field is any solution of Maxwell equations.An admissible electromagnetic field is one which can be deduced from ascalar ϕ. Let f_(uv)(ϕ) be the electromagnetic tensor F_(uv). Theelectric and magnetic vectors of ϕ, E(ϕ) and B(ϕ) respectively, are:E ₁(ϕ)=f ₀₁(ϕ), B ₁(ϕ)=½ϵ_(ijk) f _(jk)(ϕ)With this notation, the duality constraint is written as:E(ϕ)=−B(θ), B(ϕ)=E(θ)

It is necessary to characterize the Cauchy data {ϕ(r, 0), ∂_(i)ϕ(r,0),θ(r,0),∂_(i)θ(r,0)}. As was shown before, if the condition is verifiedat t=0, and is also satisfied for all t>0. In this case, the Cauchy dataand the corresponding solution of Maxwell equations are admissible.

From the two facts

i) E(ϕ) and B(ϕ) are mutually orthogonal

ii) B(ϕ) is tangent to the curves ϕ=canst and B(ϕ) is tangent toθ=canst,

It follows that these two sets of curves must be orthogonal. Let ϕ(r, 0)be any complex function with the only condition that the 1-forms dϕ anddϕ* in R³ are linearly independent. The previous condition on ϕ can bewritten as:(∇ϕ*×∇ϕ)·(∇θ*×∇θ)=0Given ϕ, is a complex PDE for the complex function θ; it has solutions(this will be used in an explicit example herein below). This gives ϕ(r,0) and θ(r, 0), and the time derivatives ∂_(t)ϕ(r, 0) and ∂_(t)θ(r, 0)are fixed by the condition above. For instance, B(θ) is a linearcombination of ∇ϕ* and ∇ϕ:B(θ)=h∇ϕ*+b*∇ϕThe function ϕ(r, 0) can be determined from ϕ(r, 0) and θ(r, 0) and,

${E\;\phi} = {\frac{1}{2\;\pi\; i} = {\frac{{{\partial_{0}\phi^{*}}{\nabla\phi}} - {{\partial_{0}\phi}{\nabla\phi^{*}}}}{( {1 + {\theta^{*}\theta}} )^{2}} = {- {B(\theta)}}}}$

The value of ∂₀ϕ can be computed. To obtain ∂_(o)θ, one can proceed inan analogous way. Therefore, there is no difficulty with the Cauchyproblem, the system having two degrees of freedom with a differentialconstraint.

Up to now, a pair of fields (ϕ, θ) have been used, but it is easy tounderstand that θ is no more than a convenience which can bedisregarded. In fact, one can forget about θ and use only the scalar ϕ,taking:L=−¼F _(uv) f ^(uv) , F _(uv) =f _(uv)(ϕ)

As Lagrangian density and accepting only Cauchy data [ϕ(r, 0),∂₀ϕ(r,0)]for which there exists an auxiliary function θ. From this point of view,the electromagnetic field would be a scalar. From now on, the θ fieldwill be considered only as an auxiliary function. The basic fieldequations of the model thus take the form:

${\partial^{u}F_{uv}} = {\sqrt{a}{\partial^{u}\lbrack {\frac{1}{2\;\pi\; i}\frac{{{\partial_{u}\phi^{*}}{\partial_{y}\phi}} - {{\partial_{y}\phi^{*}}{\partial_{u}\phi}}}{( {1 + {\phi^{*}(\phi)}^{2}} }} \rbrack}}$and are transformed into Maxwell equations.

In summary:

-   -   (1) In a theory of the fields ϕ and θ based on the Lagrangian        with the constraint, the tensors F_(αβ) and G_(αβ) defined        previously obey Maxwell equations. This means that the standard        electromagnetic theory can be derived from an underlying        structure.    -   (2) The formulas can be understood as defining a transformation:        T: ϕ→F _(uv) =F _(uv)(ϕ), θ→G _(uv) =f _(uv)(θ)    -   which transforms the highly nonlinear Euler-Lagrange equations        into Maxwell equations.    -   (3) The transformation T is not invertible, because there are        solutions of Maxwell equations H_(uv) such that T⁻¹(H_(uv)) is        not defined, that is to say, that a scalar field ϕ such that        H_(uv)==f_(uv)(ϕ) does not exist.

These solutions of Maxwell equations are not included in this theory.Also, the use of the spheres S³ and S² may remind us of Chern-Simonsterms. But, as S³ represents the physical space R³ via stereographicprojection and S² identified with the complex plane, is the space wherethe field takes values, this model does not really make use of thesekinds of terms.

As will be shown in the next section, it is not possible to distinguishbetween this model and the Maxwell one if the fields are weak. However,every ϕ solution defines at any time t a map S³→S² which has atopological charge. In this fashion, the electric E and magnetic Bfields can be represented as follows:

$B = {\Re\lbrack {\frac{1}{c}{\int_{0}^{2\omega}{\int_{0}^{\pi}\ {\int_{0}^{\infty}{( {{\hat{\varphi}\;\overset{\sim}{A}} - {\hat{\vartheta}\;\overset{\sim}{B}}} )e^{e^{{i{({{k\;{\hat{k} \cdot r}} - {\omega\; t}})}}\;}}k^{2}d\;\sin\;\vartheta\; d\;\vartheta\; d\;\varphi}}}}} \rbrack}$φ̂ = −x̂ sin   φ + ŷ cos  φϑ̂ = x̂ cos  φ cos  ϑ + ŷ sin  φ cos  ϑ − +ẑ sin  ϑk̂ = x̂ cos  φ cos  ϑ + ŷ sin  φ cos  ϑ − +ẑ sin  ϑ$E = {\Re\lbrack {\frac{E_{0}}{2_{\pi}}{\int_{0}^{2\pi}{\int_{0}^{\pi}{( {\hat{\vartheta}\;{\overset{\sim}{B}}^{\prime}\vartheta\;{\overset{\sim}{A}}^{\prime}} )e^{e^{{ik}_{0}k\;{\hat{k} \cdot r}}}\sin\;\vartheta\; d\;\vartheta\; d\;\varphi\; e^{{- i}\;\omega_{0}t}}}}} \rbrack}$$B = {\Re\lbrack {\frac{E_{0}}{2_{\pi}}{\int_{0}^{2\pi}{\int_{0}^{\pi}{( {{\vartheta\;{\overset{\sim}{A}}^{\prime}} - {\hat{\vartheta}\;{\overset{\sim}{B}}^{\prime}}} )e^{{ik}_{0}{\hat{k} \cdot r}}\sin\;\vartheta\; d\;\vartheta\;\varphi\; e^{{- i}\;\omega_{0}t}}}}} \rbrack}$${\,^{\prime}\overset{\sim}{a}} = {{- 2}i\sqrt{\pi^{3}\epsilon_{0}}( {{\hat{\varphi}\;{\overset{\sim}{A}}^{\prime}} - {\hat{\vartheta}\;{\overset{\sim}{B}}^{\prime}}} ){e^{{- i}\;\omega\; t}/{\sqrt{\hslash\;\omega}}^{\prime}}}$f^(′) = ∫₀^(π)J₁(k₀sin  ϑ n_(p)s)cos (k₀cos  ϑ n_(p)z)sin  ϑ d ϑ ${\overset{\sim}{E}}_{0}^{\prime}\frac{\mu_{0}\omega_{0}\overset{\sim}{I}\;{Me}^{{ik}_{0}n_{p}R}}{2\;\pi}$f^(′) = ∫₀^(π)J₁(k₀sin  ϑ n_(p)s)cos (k₀cos  ϑ n_(p)z)sin  ϑ d ϑ $E^{LF} \approx {{{\overset{\sim}{E}}_{0}^{\prime}}\hat{\phi}\; f^{\prime}{\cos( {{\omega_{0}\; t} - {\arg{\overset{\sim}{E}}_{0}^{\prime}}} )}}$

It is possible to create paraxial solutions using electromagnetic knotsthat produce knotted Orthogonal Orbital Angular (OAM) states. Thesestates can be muxed to achieve improvements in wireless, security,Quantum Key Distribution and quantum computing.

How to Generate Electromagnetic Knots

Referring now to FIGS. 4-6, there are illustrated various implementationof electromagnetic knot processing circuitry 402 that may be associatedwith other types of circuitry to improve signal degradation in theirassociated systems. FIG. 4 illustrates a wireless signal transmissionwherein input data 404 is first applied to wireless signal processingcircuitry 406 that uses RF signal modulation techniques for modulatingthe input data 404 on to an RF signal for transmission. The RF modulatedsignals 408 from the wireless signal processing circuitry 406 areapplied to the electromagnetic knot processing circuitry 402 as will bemore fully described hereinbelow. The electromagnetic knot processingcircuitry 402 applies electromagnetic knots to the RF modulated signal408 that provides an output electromagnetic knotted signal 410. Asdescribed previously, the knotted signals 410 within the wireless signaltransmission system will be less susceptible to fading and geometricaldispersion due to the application of the electromagnetic knots to thesignals for transmission.

FIG. 5 illustrates an optical signal transmission system wherein inputdata 412 is first applied to optical signal processing circuitry 414that uses optical signal modulation techniques for modulating the inputdata 412 on to an optical signal for transmission. The opticallymodulated signals 416 from the optical signal processing circuitry 414are applied to the electromagnetic knot processing circuitry 402 as willbe more fully described hereinbelow. The electromagnetic knot processingcircuitry 402 applies electromagnetic knots to the optically modulatedsignal 416 that provides an output electromagnetic knotted signal 416.As described previously, the knotted signals 418 within the opticalsignal transmission system will be less susceptible to fading andgeometrical dispersion due to the application of the electromagneticknots to the signals for transmission.

FIG. 6 illustrates a quantum computing system wherein input data 420 isfirst applied to quantum computing processing circuitry 422 that usesquantum computing techniques for application to the input data 420within the processing circuitry 422. The quantum computing signals 424from the quantum computing processing circuitry 422 which may be opticalor RF are applied to the electromagnetic knot processing circuitry 402.The electromagnetic knot processing circuitry 402 applieselectromagnetic knots to the quantum signals 408 that provides an outputelectromagnetic knotted signal 410. As described previously, the knottedsignals 424 within the quantum computing system will be less susceptibleto de-coherence due to the application of the electromagnetic knots tothe signals for transmission.

Referring now to FIG. 7, different methods of electromagnetic knotgeneration 402 will be required depending upon the form of disturbancerequired and the frequencies required. These forms can take the form ofring, toroidal and 3-D patch antennas in some examples. An antenna 404can be used to generate an electric ring in the radio wave (i.e.microwaves) implementations. Cylindrically polarized vector beams 706may be used to generate an electric ring. Toroidal antennas 708 may alsobe used to create electromagnetic knots. The electromagnetic waves canbe knotted using sophisticated antenna structures such as ring antennas,toroidal antennas and 3-D patch antennas. Information may then beencoded into the electromagnetic knots as the states (modulated knots).

Electromagnetic Radio Wave Knots

Referring now to FIG. 8, there is illustrated a general illustration ofthe manner for generating electromagnetic radio wave knots and FIG. 9that more fully illustrates the electrically conducting rings. Considera collection of M electrically conducting rings 804, with each ring 902concentric with the surface of a sphere 904 of radius R 906 centered atthe origin 908. A section 910 of each ring with φϵ(−Δ/2, Δ/2) removed.The ends 912 of each ring 902 connected to an alternating electriccurrent source 802 of (central) angular frequency ω₀; θ_(m) the polarangle of the mth ring (mϵ{1, . . . , M}) andI=

({tilde over (I)}e ^(−iω) ⁰ ^(t))

The (identical) current in each ring 902 is directed in the {tilde over(ϕ)} direction for I>0. Ignoring interactions between rings 902, takingeach ring to be of negligible cross-section, neglecting the radiationproduced by the elements that connect the rings to the current sourceand assuming the surrounding medium to be transparent with phaserefractive index n_(p), the electric field radiated by the rings isessentially:E ^(L)=

({tilde over (E)}^(LF) e ^(−iω) ⁰ ^(t))with each element treated as an oscillating electric dipole.

${\overset{\sim}{E}}^{LF} \approx {{\overset{\sim}{E}}_{0}\hat{\phi}\; f^{\prime}e^{{- i}\;\omega_{0}t}}$${{\overset{\sim}{E}}^{\prime}\;}_{0}\frac{\mu_{0}\omega_{0}\overset{\sim}{I}\;{Me}^{{ik}_{0}n_{p}R}}{2\pi}$f^(′) = ∫₀^(π)J₁(k₀sin  ϑ n_(p)s)cos (k₀cos  ϑ n_(p)z)sin  ϑ d ϑ$E^{LF} \approx {{{\overset{\sim}{E^{\prime}}\;}_{0}}\hat{\phi}\; f^{\prime}{\cos( {{\omega_{0}t} - {\arg\;{{\overset{\sim}{E}}^{\prime}\;}_{0}}} )}}$

Which is essentially the electric field E^(a) of the electric ring 802.The two coincide precisely in form for n_(p)≈1 so that f′=f, togetherwith a choice of phase for I such that {tilde over (E)}′₀→E₀ is real.The geometrical requirements above are reasonably well satisfied byM=100, R=1.0×10⁻¹ m and

${\frac{\omega_{0}}{2\;\pi} = {1.3 \times 10^{10}s^{- 1}}},$for example. The design can be changes to generate other unusualelectromagnetic disturbances in the radio waves.

Referring now to FIG. 10, there is provided a general block diagram ofthe structure for generating wireless electromagnetic knots using atoroidal antenna. The wireless signal processing circuitry 1002generates wireless signals using RF or optical modulation. The wirelesssignals are provided to an antenna current controller 1004 that providescontrol currents to toroidal antennas 1006 such as those describedherein below responsive to the generated wireless signals. By varyingthe applied currents from the current controller 1004 theelectromagnetic knots may be applied to the wireless signals by thetoroidal antennas 906.

Referring not to FIG. 11, there is illustrated one of the rings 902wrapped with a solenoid 1102. With respect to individual ring elements902, a solenoid 1102 can be wrapped on the ring element 902 as shown inFIG. 11 and control the electromagnetic knots based on homotopy classes.Each of the rings 902 having the solenoid 1102 wrapped around it may bestacked on top of one another to form the sphere structure 1202generally illustrated in FIG. 12.

Referring now to FIGS. 13 and 14 there are illustrated moresophisticated structure antennas. The ring like structures 1302, 1402illustrate knotted toroids that would also have solenoids wrapped aroundthem in a similar manner to the rings.

Referring now to FIG. 15 there is illustrated a further possibleimplementations for generating electromagnetic knots whereinthree-dimensional patch antennas are used for applying theelectromagnetic knots to a signal. The patch antennas may be similar tothose described in U.S. patent applicaiton Ser. No. 16/037,550, issuedon Jul. 17, 2018, entitled PATCH ANTENNA ARRAY FOR TRANSMISSION OFHERMITE-GAUSSIAN AND LAGUERRE GAUSSIAN BEAMS, which is incorporatedherein by reference in its entirety. FIG. 15 illustrates a wirelesssignal transmission wherein input data 1502 is first applied to wirelesssignal processing circuitry 1504 that uses RF signal modulationtechniques for modulating the input data 1502 on to an RF signal fortransmission. The RF modulated signals 1306 from the wireless signalprocessing circuitry 1504 are applied to the three-dimensional patchantenna array 1508 for applying the electromagnetic knot to the RFsignal to provide an output electromagnetic knotted signal 1510. Withinthe patch antenna array 1508, multiple patch antennas can be configuredin circular, elliptical or mixed configuration to generateelectromagnetic knots. Each component of the patch antenna array wouldhave a different phase applied thereto to produce the knottedEigen-channels. Additionally, multiple layers of antennas can beoverlayed to naturally mux the independent modes using theelectromagnetic knots. These structures are more fully described inFIGS. 16-21 below. Designs and simulations of the EM knots can beperformed using ANSYS HFSS with micro-strip feed structure to preparefor manufacturing. Cleanroom and lithography process are used to buildthe 3D structure of patch antennas that produce EM knots.

FIG. 16 illustrates a multilayer patch antenna array 1602 that may beelectromagnetic knot transmissions. The multilayer patch antenna array1602 includes a first antenna layer 1604 for transmitting a firstordered beam, a second antenna layer 1606 for transmitting a secondordered beam and a third layer 1608 for transmitting a third orderedbeam. Each of the layers 1604, 1606 and 1608 are stacked on a samecenter. While the present embodiment is illustrated with respect to amultilayer patch antenna array 1602 including only three layers, itshould be realized that either more or less layers may be implemented ina similar fashion as described herein. On the surface of each of thelayers 1604, 1606 and 1608 are placed patch antennas 1610. Each of thepatch antennas are placed such that they are not obscured by the abovelayer. The layers 1604, 1606 and 1608 are separated from each other bylayer separator members 1612 that provide spacing between each of thelayers 1604, 1606 and 1608. The configuration of the layers of the patchantenna may be in rectangular, circular or elliptical configurations togenerate Hermite-Gaussian, Laguerre-Gaussian or Ince-Gaussian beams.

The patch antennas 1610 used within the multilayer patch antenna array1602 are made from FR408 (flame retardant 408) laminate that ismanufactured by Isola Global, of Chandler Ariz. and has a relativepermittivity of approximately 3.75. The antenna has an overall height of125 μm. The metal of the antenna is copper having a thickness ofapproximately 12 μm. The patch antenna is designed to have an operatingfrequency of 73 GHz and a free space wavelength of 4.1 mm. Thedimensions of the input 50 Ohm line of the antenna is 280 μm while theinput dimensions of the 100 Ohm line are 66 μm.

Each of the patch antennas 1610 are configured to transmit signals at apredetermined phase that is different from the phase of each of theother patch antenna 1610 on a same layer. Thus, as further illustratedin FIG. 18, there are four patch antenna elements 1610 included on alayer 1604. Each of the antenna elements 1604 have a separate phaseassociated there with as indicated in FIG. 18. These phases include π/2,2(π/2), 3(π/2) and 4(π/2). Similarly, as illustrated in FIG. 19 layer1606 includes eight different patch antenna elements 1610 including thephases π/2, 2(π/2), 3(π/2), 4(π/2), 5(π/2), 6(π/2), 7(π/2) and 8(π/2) asindicated. Finally, referring back to FIG. 16, there are included 12patch antenna elements 1610 on layer 1608. Each of these patch antennaelements 1610 have a phase assigned thereto in the manner indicated inFIG. 16. These phases include π/2, 2(π/2), 3(π2), 4(π/2), 5(π/2),6(π/2), 7(π/2), 8(π/2), 9(π/2), 10(π/2), 11(π/2) and 12(π/2).

Each of the antenna layers 1604, 1606 and 1608 are connected to acoaxial end-launch connector 1616 to feed each layer of the multilayerpatch antenna array 1602. Each of the connectors 1616 are connected toreceive a separate signal that allows the transmission of a separateordered antenna beam in a manner similar to that illustrated in FIG. 17.The emitted beams are multiplexed together by the multilayered patchantenna array 1602. The orthogonal wavefronts transmitted from eachlayer of the multilayered patch antenna array 1602 in a spatial mannerto increase capacity as each wavefront will act as an independent Eigenchannel. The signals are multiplexed onto a single frequency andpropagate without interference or crosstalk between the multiplexedsignals. While the illustration with respect to FIG. 17 illustrates thetransmission of OAM beams at OAM 1, OAM 2 and OAM 3 ordered levels.

It should be understood that other types of Hermite Gaussian andLaguerre Gaussian beams can be transmitted using the multilayer patchantenna array 1602 illustrated. Hermite-Gaussian polynomials andLaguerre-Gaussian polynomials are examples of classical orthogonalpolynomial sequences, which are the Eigenstates of a quantum harmonicoscillator. However, it should be understood that other signals may alsobe used, for example orthogonal polynomials or functions such as Jacobipolynomials, Gegenbauer polynomials, Legendre polynomials and Chebyshevpolynomials. Legendre functions, Bessel functions, prolate spheroidalfunctions and Ince-Gaussian functions may also be used. Q-functions areanother class of functions that can be employed as a basis fororthogonal functions.

The feeding network 1618 illustrated on each of the layers 1604, 1606,1608 uses delay lines of differing lengths in order to establish thephase of each patch antenna element 1610. By configuring the phases asillustrated in FIGS. 16-18 the OAM beams of different orders aregenerated and multiplexed together.

Referring now to FIG. 20, there is illustrated a transmitter 2002 forgenerating a multiplexed beam for transmission. As discussed previously,the multilayered patch antenna array 1602 includes a connector 1616associated with each layer 1604, 1606, 1608 of the multilayer patchantenna array 1602. Each of these connectors 1616 are connected withsignal generation circuitry 2004. The signal generation circuitry 2004includes, in one embodiment, a 60 GHz local oscillator 2006 forgenerating a 60 GHz carrier signal. The signal generation circuit 2004may also work with other frequencies, such as 70/80 GHz. The 60 GHzsignal is output from the local oscillator 2006 to a power dividercircuit 2008 which separates the 60 GHz signal into three separatetransmission signals. Each of these separated transmission signals areprovided to an IQ mixer 2010 that are each connected to one of the layerinput connectors 1616. The IQ mixer circuits 2010 are connected to anassociated additive white Gaussian noise circuit 2012 for inserting anoise element into the generated transmission signal. The AWG circuit2012 may also generate SuperQAM signals for insertion in to thetransmission signals. The IQ mixer 2010 generates signals in a mannersuch as that described in U.S. Pat. No. 9,331,875, issued on May 3,2016, entitled SYSTEM AND METHOD FOR COMMUNICATION USING ORBITAL ANGULARMOMENTUM WITH MULTIPLE LAYER OVERLAY MODULATION, which is incorporatedherein by reference in its entirety.

Using the transmitter 2002 illustrated in FIG. 20. A multiplexed beam(Hermite Gaussian, Laguerre Gaussian, etc.) can be generated asillustrated in FIG. 21. As illustrated, the multilayered patch antennaarray 1602 will generate a multiplexed beam 2102 for transmission. Inthe present example, there is illustrated a multiplex OAM beam that hastwists for various order OAM signals in a manner similar to thatdisclosed in U.S. Pat. No. 9,331,875. An associated receiver detectorwould detect the various OAM rings 604 as illustrated each of the ringsassociated with a separate OAM processed signal.

Referring now to FIG. 22, there is illustrated a receiver 2202 fordemultiplexing signals received from a multiplexed signal generatedusing the transmitter 2002 of FIG. 20. The receiver 2202 includes amultilayer patch antenna array 1602 such as that described herein above.The multilayer patch antenna array 1602 receives the incomingmultiplexed signal 2204 and each layer 1604, 1606, and 1608 of theantenna array 1602 will extract a particular order of the receivedmultiplexed signal from each of the connector outputs 1616 of aparticular layer. The signals from each of the connectors 1616 areapplied to a mixer circuit 2206 that demultiplexes the received signalin a manner similar to that discussed with respect to U.S. patentapplication Ser. No. 14/323,082 using a 60 GHz local oscillator signalfrom oscillator 2208. The demultiplexed signal may then be read using,for example, a real-time oscilloscope 2210 or other signal readingdevice. Each of the three transmitted signals is thus decoded at thereceiver 2202 that were transmitted in each of the ordered OAM signalsreceived from the transmitters 2102. In a further embodiment, ademultiplexing approach using SPP (spiral phase plate) may also beapplied to detect OAM channels.

The signals transmitted by the transmitter 2002 or the receiver 2202 maybe used for the transmission of information between two locations in avariety of matters. These include there use in both front haulcommunications and back haul communications within a telecommunicationsor data network.

As described previously, the knotted signals 1510 (FIG. 15) within thewireless signal transmission system will be less susceptible to fadingand geometrical dispersion due to the application of the electromagneticknots to the signals for transmission. The patch antenna array anddesign may in one embodiment comprises the patch antenna arraysdescribed in U.S. patent application Ser. No. 15/960,904, entitledSYSTEM AND METHOD FOR COMBINING MIMO AND MODE-DIVISION MULTIPLEXING,filed on Apr. 24, 2018, which is incorporated herein by reference in itsentirety.

In addition to the RF wireless versions described above other types ofsystem may be used for generating electromagnetic knots in otheroperating environments. Qubit signals in quantum computing system can begenerated using electromagnetic knots in photonics using polarizationstates of the signals in system such as those described in U.S. patentapplication Ser. No. 16/509,301, entitled UNIVERSAL QUANTUM COMPUTER,COMMUNICATION, QKD SECURITY AND QUANTUM NETWORKS USING OAM QU-DITS WITHDLP, filed on Jul. 11, 2019, which is incorporated herein by referencein its entirety. Knotted OAM states can be generated using bothphotonics and electromagnetic waves such as those described in U.S.patent application Ser. No. 14/882,085, entitled APPLICATION OF ORBITALANGULAR MOMENTUM TO FIBER, FSO AND RF, filed on Oct. 13, 2015, which isincorporated herein by reference in its entirety.

Referring now to FIGS. 23-25 there are illustrated a number of otherimplementations of the knotted signal processing. FIG. 23 illustrates asystem wherein multiple signals are input to OAM processing circuitry2302 that applies an orbital angular momentum to the signals. The OAMprocessed signals are applied to knotted processing circuitry 2304 thatapplies electromagnetic knots to the OAM signals using one of thetechniques described herein. Each of the knotted beams may carry adifferent message signal. The knotted OAM processed signals may be muxedtogether using multiplexing circuitry 2306. The multiplexing circuitrymay mux the signals by the multiplexing circuitry 2306 at a specificradio frequency. The multiplexed knotted OAM circuitry may betransmitted from a transmitter to a receiver, and the signal isdemultiplexed into the knotted OAM processed signals usingdemultiplexing circuitry 2308. The demultiplexed signals are applied tothe knotted processing circuitry 2310 to remove the previously appliedelectromagnetic knots from the signal. The de-knotted signals arefinally applied to the OAM processing circuitry 2312 to remove theorbital angular momentum from each of the signals.

FIG. 24 illustrates how OAM knotted beams 2402 or muxed OAM knottedbeams each carrying different signals may be multiplexed with differentradio channels 2404 by multiplexing circuitry 2406 for transmission.

FIG. 25 illustrates knot division multiplexing circuitry 2502 forreceiving multiple input signals 2504 to generate a knotted multiplexedoutput 2506. The knot division multiplexing (KDM) can combine thesignals on a single frequency. KDM may be applied in both Backhaul andFronthaul scenarios to improve their operation. The KDM processedsignals may further be transmitted using MIMO techniques in acompactified massive MIMO system such as that disclosed in U.S. patentapplication Ser. No. 15/960,904, entitled SYSTEM AND METHOD FORCOMBINING MIMO AND MODE-DIVISION MULTIPLEXING, filed on Apr. 24, 2018,which is incorporated herein by reference in its entirety.

As described above path loss can degrade an electromagnetic signal.Other than path loss degradation of electromagnetic signals (due togeometrical dispersion), channel effects can also degrade theinformation signal (channel conditions). As discussed herein,environmental degradations can never open the electromagnetic knots. Theelectromagnetic knots may be used in a number of applications includingall communications in wireless and fiber, radar, wearable using lasersand biomedical devices.

In topological quantum computers, the Schrodinger wave function or stateis knotted via a sophisticated braiding process that preserves thetopological features (wave knots) in the presence of noise (critical forquantum computing). Therefore, one has to encode information into theelectromagnetic knots before transmission. Various applications of wavefunction knots include quantum computing, quantum communications andnetworks, quantum informatics, cyber security and condensed matter orsolid states.

The mathematical foundation of the above is a new algebra (CliffordAlgebra) which generalizes quaternions and its relationship withelectromagnetic knots as well as braid group representations related toMajorana fermions. This algebra is a non-Abelian algebra where suchknots can be generated. These braiding representations have importantapplications in quantum informatics and topology. There is one algebradescribing both electromagnetic knots as well as Majorana operators.They are intimately connected to SU(2) symmetry groups in group theory.A new formulation of electromagnetism in SU(2) symmetry can describeover half a dozen observed electromagnetic phenomenon where traditionaltheory in U(1) symmetry cannot. That is the braiding of Majoranafermions as well as electromagnetic knots happen by naturalrepresentations of Clifford algebras and also with the representationsof the quaternions as SU(2) to the braid group and electromagneticknots.

It will be appreciated by those skilled in the art having the benefit ofthis disclosure that this electromagnetic knots and its applications inradio waves for wireless transmissions and photonics for quantumcomputing provides an improved manner for limiting signal degradation tosignals in wireless systems and quantum computing. It should beunderstood that the drawings and detailed description herein are to beregarded in an illustrative rather than a restrictive manner, and arenot intended to be limiting to the particular forms and examplesdisclosed. On the contrary, included are any further modifications,changes, rearrangements, substitutions, alternatives, design choices,and embodiments apparent to those of ordinary skill in the art, withoutdeparting from the spirit and scope hereof, as defined by the followingclaims. Thus, it is intended that the following claims be interpreted toembrace all such further modifications, changes, rearrangements,substitutions, alternatives, design choices, and embodiments.

What is claimed is:
 1. A system for transmitting signals, comprising:processing circuitry for receiving at least one input signal fortransmission from the processing circuitry to a second location;electromagnetic knot processing circuitry for receiving processedsignals from the processing circuitry for applying an electromagneticknot to the received processed signal before transmission to the secondlocation; and wherein a first signal degradation caused by environmentalfactors of the electromagnetic knot processed signal is improved over asecond signal degradation caused by the environmental factors of asignal not including the electromagnetic knot, wherein the first andsecond signal degradation comprises signal de-coherence.
 2. The systemof claim 1, wherein the processing circuitry comprises wireless signalmodulation circuitry for modulating the at least one input signal fortransmission from the wireless signal modulation circuitry to the secondlocation.
 3. The system of claim 2, wherein the first and second signaldegradation comprises at least one of signal fading and geometricaldispersion.
 4. The system of claim 1, wherein the processing circuitrycomprises optical signal modulation circuitry for modulating the atleast one input signal for transmission from the optical signalmodulation circuitry to the second location.
 5. The system of claim 1,wherein the processing circuitry comprises a quantum computing circuitfor generating a quantum signal responsive to the at least one inputsignal for transmission from the quantum computing circuit to the secondlocation.
 6. The system of claim 1, wherein the electromagnetic knotprocessing circuitry further comprises: a plurality of toroidal antennasconnected to receive the processed signal from the processing circuitry,wherein the plurality of toroidal antennas apply the electromagneticknot to the at least one input sign to generate the electromagnetic knotprocessed signal responsive to a current control signal; and an antennacurrent controller for generating the current control signal to controlthe application of the electromagnetic knot to the electromagnetic knotprocessed signal.
 7. The system of claim 6, wherein the plurality oftoroidal antennas comprise a plurality of rings each ring having asolenoid wrapped around the ring, the plurality of rings stacked on topof one another to provide a substantially sphere shape.
 8. The system ofclaim 1, wherein the electromagnetic knot processing circuitry furthercomprise: a knotted toroid; and a solenoid wrapped around the knottedtoroid.
 9. The system of claim 1, wherein the electromagnetic knotprocessing circuitry further comprises a three dimensional patch antennaarray for applying the electromagnetic knot to the received processedsignal.
 10. The system of claim 9, wherein the three dimensional patchantenna array further comprises: a plurality of patch antennas; aplurality of layers, each of the plurality of layers separated from eachother by a distance, each of the plurality of layers further supportinga portion of the plurality of patch antennas; a plurality of connectors,each of the plurality of connectors associated with one of the pluralityof layers, for supplying a signal for transmission by the associatedlayer; and a feed network on each of the plurality of layers forproviding a connection between a connector of the plurality ofconnectors associated with the layer and the portion of the plurality ofpatch antennas located on the layer, wherein a length of the connectionbetween the connector and each of the portion of the plurality of patchantennas applies a different phase to each of the portion of theplurality of patch antennas on the layer.
 11. The system of claim 1further comprising orbital angular momentum processing circuitry forapplying an orbital angular momentum to the at least one input signal.12. The system of claim 1, wherein the processing circuitry comprises atleast one of RF processing circuitry and photonic processing circuitry.13. A method for transmitting signals, comprising: receiving at leastone input signal for transmission from a processing circuitry to asecond location; applying an electromagnetic knot to the receivedprocessed signal before transmission to the second location usingelectromagnetic knot processing circuitry; and wherein a first signaldegradation caused by environmental factors of the electromagnetic knotprocessed signal is improved over a second signal degradation caused bythe environmental factors of a signal not including the electromagneticknot, wherein the first and second signal degradation comprises signalde-coherence.
 14. The method of claim 13 modulating the at least oneinput signal for transmission from the processing circuitry to thesecond location using signal modulation circuitry.
 15. The method ofclaim 14, wherein the first and second signal degradation comprises atleast one of signal fading and geometrical dispersion.
 16. The method ofclaim 13 modulating the at least one input signal for transmission tothe second location using optical signal modulation circuitry.
 17. Themethod of claim 13 generating a quantum signal responsive to the atleast one input signal for transmission from a quantum computing circuitto the second location.
 18. The method of claim 13, wherein the step ofapplying further comprises: applying the electromagnetic knot to the atleast one input sign to generate the electromagnetic knot processedsignal responsive to a current control signal provided to a plurality oftoroidal antennas; and generating the current control signal to controlthe application of the electromagnetic knot to the electromagnetic knotprocessed signal using an antenna current controller.
 19. The method ofclaim 18, wherein the plurality of toroidal antennas comprise aplurality of rings each ring having a solenoid wrapped around the ring,the plurality of rings stacked on top of one another to provide asubstantially sphere shape.
 20. The method of claim 13, wherein the stepof applying further comprises applying the electromagnetic knot to theat least one input sign to generate the electromagnetic knot processedsignal using a solenoid wrapped knotted toroid.
 21. The method of claim13, wherein the step of applying further comprises applying theelectromagnetic knot to the at least one input sign to generate theelectromagnetic knot processed signal using a three dimensional patchantenna array.
 22. The method of claim 13 further comprising applying anorbital angular momentum to the at least one input signal using orbitalangular momentum processing circuitry.
 23. The method of claim 13,wherein the at least one input signal comprises at least one of an RFsignal and a photonic signal.
 24. A system for transmitting signals,comprising: wireless signal modulation circuitry for receiving at leastone input signal and modulating the at least one input signal fortransmission from the wireless signal modulation circuitry to a secondlocation; electromagnetic knot processing circuitry for receivingprocessed signals from the wireless signal modulation circuitry forapplying an electromagnetic knot to the received processed signal beforetransmission to the second location, wherein the electromagnetic knotprocessing circuitry further comprises: a plurality of toroidal antennasconnected to receive the processed signal from the wireless signalmodulation circuitry, wherein the plurality of toroidal antennas applythe electromagnetic knot to the at least one input signal to generatethe electromagnetic knot processed signal responsive to a currentcontrol signal; an antenna current controller for generating the currentcontrol signal to control the application of the electromagnetic knot tothe electromagnetic knot processed signal; and wherein a first signaldegradation caused by environmental factors of the electromagnetic knotprocessed signal is improved over a second signal degradation caused bythe environmental factors of a signal not including the electromagneticknot.
 25. The system of claim 24, wherein the first and second signaldegradation comprises at least one of signal fading and geometricaldispersion.
 26. The system of claim 24, wherein the plurality oftoroidal antennas comprise a plurality of rings each ring having asolenoid wrapped around the ring, the plurality of rings stacked on topof one another to provide a substantially sphere shaped antenna.
 27. Asystem for transmitting signals, comprising: wireless signal modulationcircuitry for receiving at least one input signal and modulating the atleast one input signal for transmission from the wireless signalmodulation circuitry to a second location; electromagnetic knotprocessing circuitry for receiving processed signals from the wirelesssignal modulation circuitry for applying an electromagnetic knot to thereceived processed signal before transmission to the second location,wherein the electromagnetic knot processing circuitry further comprisesa three dimensional patch antenna array for applying the electromagneticknot to the received processed signal comprising: a plurality of patchantennas; a plurality of layers, each of the plurality of layersseparated from each other by a distance, each of the plurality of layersfurther supporting a portion of the plurality of patch antennas; aplurality of connectors, each of the plurality of connectors associatedwith one of the plurality of layers, for supplying a signal fortransmission by the associated layer; a feed network on each of theplurality of layers for providing a connection between a connector ofthe plurality of connectors associated with the layer and the portion ofthe plurality of patch antennas located on the layer, wherein a lengthof the connection between the connector and each of the portion of theplurality of patch antennas applies a different phase to each of theportion of the plurality of patch antennas on the layer; and wherein afirst signal degradation caused by environmental factors of theelectromagnetic knot processed signal is improved over a second signaldegradation caused by the environmental factors of a signal notincluding the electromagnetic knot.
 28. The system of claim 27, whereinthe first and second signal degradation comprises at least one of signalfading and geometrical dispersion.
 29. A system for transmittingsignals, comprising: processing circuitry for receiving at least oneinput signal for transmission from the processing circuitry to a secondlocation; electromagnetic knot processing circuitry for receivingprocessed signals from the processing circuitry for applying anelectromagnetic knot to the received processed signal beforetransmission to the second location, wherein the electromagnetic knotprocessing circuitry further comprises: a knotted toroid; a solenoidwrapped around the knotted toroid; and wherein a first signaldegradation caused by environmental factors of the electromagnetic knotprocessed signal is improved over a second signal degradation caused bythe environmental factors of a signal not including an electromagneticknot.
 30. A system for transmitting signals, comprising: processingcircuitry for receiving at least one input signal for transmission fromthe processing circuitry to a second location, wherein the processingcircuitry comprises a quantum computing circuit for generating a quantumsignal responsive to the at least one input signal for transmission fromthe quantum computing circuit to the second location; electromagneticknot processing circuitry for receiving processed signals from theprocessing circuitry for applying an electromagnetic knot to thereceived processed signal before transmission to the second location;and wherein a first signal degradation caused by environmental factorsof the electromagnetic knot processed signal is improved over a secondsignal degradation caused by the environmental factors of a signal notincluding an electromagnetic knot.
 31. The system of claim 30, whereinthe quantum computing circuit generates topological features that limitseffects of the environmental factors.